Imaging a Quasar Accretion Disk with Microlensing

We show how analysis of a quasar high-magnification microlensing event may be used to construct a map of the frequency-dependent surface brightness of the quasar accretion disk. The same procedure also allows determination of the disk inclination angle, the black hole mass (modulo the caustic velocity), and possibly the black hole spin. This method depends on the validity of one assumption: that the optical and ultraviolet continuum of the quasar is produced on the surface of an azimuthally symmetric, flat equatorial disk, whose gas follows prograde circular orbits in a Kerr spacetime (and plunges inside the marginally stable orbit). Given this assumption, we advocate using a variant of first-order linear regularization to invert multi-frequency microlensing lightcurves to obtain the disk surface brightness as a function of radius and frequency. The other parameters can be found by minimizing χ in a fashion consistent with the regularized solution for the surface brightness. We present simulations for a disk model appropriate to the Einstein Cross quasar, an object uniquely well-suited to this approach. These simulations confirm that the surface brightness can be reconstructed quite well near its peak, and that there are no systematic errors in determining the other model parameters. We also discuss the observational requirements for successful implementation of this technique. Subject headings: accretion, accretion disks — gravitational lensing — quasars: individual (2237+0305) — relativity